where we used that \(f_q = f_{-q}^*\)  and that \(f_0 = 1\) . Note the
similarity of the \(C_1\)  and \(C_2\)  in Eq. (REF ) to the
Resta [1]} and Resta-Sorella [2]} expressions for
the polarization and its variance. In the limit \(L\rightarrow \infty \) 
\(C_1\)  and \(C_2\)  converge to \(\langle x \rangle \)  and \(\langle x^2\rangle - \langle x \rangle ^2\) , respectively, and higher order
cumulants constructed via Eq. (REF ) also reproduce the
cumulants (Eq. (REF )).
